Finite‐time stability and finite‐time weighted
            <i>L</i>
            <sub>2</sub>
            ‐gain analysis for switched systems with time‐varying delay

Lin, Xiangze; Du, Haibo; Li, Shihua; Zou, Yun

doi:10.1049/iet-cta.2012.0551

Cited by 84 publications

(72 citation statements)

References 58 publications

(68 reference statements)

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“…then under any switching signal ( ) k σ with the average dwell time scheme (29), the closed-loop system (38) is H ∞ finite-time bounded with respect to 1 2 ( , , , ,…”

Section: Finite-time H ∞ Controlmentioning

confidence: 99%

“…Recently, a few results on finite-time stability of switched systems have been given in [22,23]. Some results on finite-time H ∞ control for switched systems have been reported in the literature [24][25][26][27][28][29]. However, to the best of our knowledge, there are few results available on finite-time stability and finite-time boundedness of delta operator switched systems with time-varying delay, and this is the motivation for our study.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

Qin

Xiang

Karimi

2014

Int. J. Control Autom. Syst.

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Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach is investigated in this paper. Firstly, by using the average dwell time approach and delta operator theory, sufficient conditions for H ∞ finite-time boundedness of the underlying systems are derived. Then a state feedback controller is proposed such that the resulting closed-loop system is H ∞ finitetime bounded. All the obtained results are formulated in terms of linear matrix inequalities (LMIs). Finally, an example is presented to show the validity of the proposed results.

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“…then under any switching signal ( ) k σ with the average dwell time scheme (29), the closed-loop system (38) is H ∞ finite-time bounded with respect to 1 2 ( , , , ,…”

Section: Finite-time H ∞ Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

Qin

Xiang

Karimi

2014

Int. J. Control Autom. Syst.

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“…In the past few years, finite-time control issues have become a hot topic due to their wide applications in practical engineering, such as switched systems [1][2][3], Markovian jump systems [4,5], singular systems [6], etc. For real industrial systems, it is usually required that the values of the system states should not exceed some given level in a certain time interval, avoiding the saturations of the sensors or damages to the equipments caused by the excitation of nonlinear dynamics [7].…”

Section: Introductionmentioning

confidence: 99%

Robust H∞ Finite-Time Control for Discrete Markovian Jump Systems with Disturbances of Probabilistic Distributions

Chen

Liu

Zhang

2015

Entropy

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This paper is concerned with the robust H ∞ finite-time control for discrete delayed nonlinear systems with Markovian jumps and external disturbances. It is usually assumed that the disturbance affects the system states and outputs with the same influence degree of 100%, which is not evident enough to reflect the situation where the disturbance affects these two parts by different influence degrees. To tackle this problem, a probabilistic distribution denoted by binomial sequences is introduced to describe the external disturbance. Throughout the paper, the definitions of the finite-time boundedness (FTB) and the H ∞ FTB are firstly given respectively. To extend the results further, a model which combines a linear dynamic system and a static nonlinear operator is referred to describe the system under discussion. Then by virtue of state feedback control method, some new sufficient criteria are derived which guarantee the FTB and H ∞ FTB performances for the considered system. Finally, an example is provided to demonstrate the effectiveness of the developed control laws.

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“…[7], FTS analysis and control problems were discussed for many kinds of linear systems. Recently, due to the importance in the study of the transient behavior of systems, FTS has been introduced into many different fields, such as nonlinear systems [8,9], stochastic systems [10,11], singular systems [12][13][14], time-delay systems [15,16], fractional order systems [17], and switched systems [18][19][20], and many related results have been obtained.…”

Section: Introductionmentioning

confidence: 99%

“…It is noticed that Eq. (20) in Corollary 1 can be easily turned into a series of LMI conditions. Therefore, based on the CCL approach, an iterative algorithm similar to Algorithm 1 can be employed to design the desired non-negative controller.…”

mentioning

confidence: 99%

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

Xue

2014

Journal of Dynamic Systems, Measurement, and Control

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In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

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Finite‐time stability and finite‐time weighted L ₂ ‐gain analysis for switched systems with time‐varying delay

Cited by 84 publications

References 58 publications

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

Robust H∞ Finite-Time Control for Discrete Markovian Jump Systems with Disturbances of Probabilistic Distributions

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

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Finite‐time stability and finite‐time weighted L 2 ‐gain analysis for switched systems with time‐varying delay

Cited by 84 publications

References 58 publications

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

Robust H∞ Finite-Time Control for Discrete Markovian Jump Systems with Disturbances of Probabilistic Distributions

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

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Finite‐time stability and finite‐time weighted L ₂ ‐gain analysis for switched systems with time‐varying delay